Ok, I wanted to ask the experts on this one

Im given that a square is a quadrilateral that is equilateral and equiangular.

Im asked to find 3 different characterizations of a square. I came up with the following biconditionals but dont know if there true both ways/

1.A Polygon is a square IFF it is a equilateral rectangle where every angle is a right angle.

2.Same as above Except a Parallelogram where every etc..

3.Same as above Except Rhombus

Would these be correct?

Thank you for your time and help